It should be possible using sockets [needs policy].
There’s no magic settings for the WWW class. I’d try experimenting with it [e.g. can one reuse an instance of WWW [doubt it]? What actually happens if you create many - does unity work magic behind the scenes?] - but I’ve not heard of it working.
I was wondering whether WWW does that on its own or not - would be great to hear from Unity employees if that is the case.
Regarding sending requests by communication with the web page - have you any idea what would be the performance impacts of that? Performance might be hindered in a way that would make the whole thing not worth while.